Question: Simplify the following expression: $ z = \dfrac{p - 10}{7p + 9} - \dfrac{-5}{8} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{8}{8}$ $ \dfrac{p - 10}{7p + 9} \times \dfrac{8}{8} = \dfrac{8p - 80}{56p + 72} $ Multiply the second expression by $\dfrac{7p + 9}{7p + 9}$ $ \dfrac{-5}{8} \times \dfrac{7p + 9}{7p + 9} = \dfrac{-35p - 45}{56p + 72} $ Therefore $ z = \dfrac{8p - 80}{56p + 72} - \dfrac{-35p - 45}{56p + 72} $ Now the expressions have the same denominator we can simply subtract the numerators: $z = \dfrac{8p - 80 - (-35p - 45) }{56p + 72} $ Distribute the negative sign: $z = \dfrac{8p - 80 + 35p + 45}{56p + 72}$ $z = \dfrac{43p - 35}{56p + 72}$